论文标题
对三值Lukasiewicz逻辑的某些含义片段的一阶版本的代数研究
An algebraic study of the first order version of some implicational fragments of the three-valued Lukasiewicz logic
论文作者
论文摘要
MV-Elgebras是有限链产生的Lukasiewicz逻辑的代数语义和MV-Elgebras，这是Heything代数，其中可以用De Morgan和Moisil的模态操作员来写下神的含义。在我们的工作中，研究了三价Lukasiewicz逻辑的片段。提出了命题和一阶逻辑。在这两种情况下，最大一致的理论都被研究为Lindenbaum-Tarski代数的Monteiro的最大扣除系统。因此，证明了相对于合适的代数结构的充分定理。
MV-algebras are an algebraic semantics for Lukasiewicz logic and MV-algebras generated by a finite chain are Heyting algebras where the Godel implication can be written in terms of De Morgan and Moisil's modal operators. In our work, a fragment of trivalent Lukasiewicz logic is studied. The propositional and first-order logic is presented. The maximal consistent theories are studied as Monteiro's maximal deductive systems of the Lindenbaum-Tarski algebra, in both cases. Consequently, the adequacy theorem with respect to the suitable algebraic structures is proven.
